On the large amplitude free vibrations of axially loaded Euler-Bernoulli beams

	Steel and Composite Structures Volume 14, Number 1, January 2013, pages 73-83 DOI: http://dx.doi.org/10.12989/scs.2013.14.1.073
	On the large amplitude free vibrations of axially loaded Euler-Bernoulli beams
	Mahmoud Bayat, Iman Pakar and Mahdi Bayat
Abstract [Full Text]
	In this paper Hamiltonian Approach (HA) have been used to analysis the nonlinear free vibration of Simply-Supported (S-S) and for the Clamped-Clamped (C-C) Euler-Bernoulli beams fixed at one end subjected to the axial loads. First we used Galerkin\'s method to obtain an ordinary differential equation from the governing nonlinear partial differential equation. The effect of different parameter such as variation of amplitude to the obtained on the non-linear frequency is considered. Comparison of HA with Runge-Kutta 4th leads to highly accurate solutions. It is predicted that Hamiltonian Approach can be applied easily for nonlinear problems in engineering.
Key Words
	non-linear vibration, analytical solution, beam vibration, Runge-Kutta 4th
Address
	Mahmoud Bayat, Iman Pakar and Mahdi Bayat: Department of Civil Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran